Real
TensorMechanicsPlasticOrthotropic::yieldFunction(const RankTwoTensor & stress, Real intnl) const
{
const RankTwoTensor j2prime = _l1 * stress;
const RankTwoTensor j3prime = _l2 * stress;
return _b * stress.trace() +
std::pow(std::pow(-j2prime.generalSecondInvariant(), 3.0 / 2.0) - j3prime.det(),
1.0 / 3.0) -
yieldStrength(intnl);
}
Real
TensorMechanicsPlasticJ2::yieldFunction(const RankTwoTensor & stress, Real intnl) const
{
return std::sqrt(3.0 * stress.secondInvariant()) - yieldStrength(intnl);
}
bool
TensorMechanicsPlasticJ2::returnMap(const RankTwoTensor & trial_stress,
Real intnl_old,
const RankFourTensor & E_ijkl,
Real ep_plastic_tolerance,
RankTwoTensor & returned_stress,
Real & returned_intnl,
std::vector<Real> & dpm,
RankTwoTensor & delta_dp,
std::vector<Real> & yf,
bool & trial_stress_inadmissible) const
{
if (!(_use_custom_returnMap))
return TensorMechanicsPlasticModel::returnMap(trial_stress,
intnl_old,
E_ijkl,
ep_plastic_tolerance,
returned_stress,
returned_intnl,
dpm,
delta_dp,
yf,
trial_stress_inadmissible);
yf.resize(1);
Real yf_orig = yieldFunction(trial_stress, intnl_old);
yf[0] = yf_orig;
if (yf_orig < _f_tol)
{
// the trial_stress is admissible
trial_stress_inadmissible = false;
return true;
}
trial_stress_inadmissible = true;
Real mu = E_ijkl(0, 1, 0, 1);
// Perform a Newton-Raphson to find dpm when
// residual = 3*mu*dpm - trial_equivalent_stress + yieldStrength(intnl_old + dpm) = 0
Real trial_equivalent_stress = yf_orig + yieldStrength(intnl_old);
Real residual;
Real jac;
dpm[0] = 0;
unsigned int iter = 0;
do
{
residual = 3.0 * mu * dpm[0] - trial_equivalent_stress + yieldStrength(intnl_old + dpm[0]);
jac = 3.0 * mu + dyieldStrength(intnl_old + dpm[0]);
dpm[0] += -residual / jac;
if (iter > _max_iters) // not converging
return false;
iter++;
} while (residual * residual > _f_tol * _f_tol);
// set the returned values
yf[0] = 0;
returned_intnl = intnl_old + dpm[0];
RankTwoTensor nn = 1.5 * trial_stress.deviatoric() /
trial_equivalent_stress; // = dyieldFunction_dstress(trial_stress, intnl_old) =
// the normal to the yield surface, at the trial
// stress
returned_stress = 2.0 / 3.0 * nn * yieldStrength(returned_intnl);
returned_stress.addIa(1.0 / 3.0 * trial_stress.trace());
delta_dp = nn * dpm[0];
return true;
}
void YieldStrength<EvalT, Traits>::
evaluateFields(typename Traits::EvalData workset)
{
bool print = false;
//if (typeid(ScalarT) == typeid(RealType)) print = true;
if (print)
std::cout << " *** YieldStrength *** " << std::endl;
int numCells = workset.numCells;
if (is_constant) {
for (int cell=0; cell < numCells; ++cell) {
for (int qp=0; qp < numQPs; ++qp) {
yieldStrength(cell,qp) = constant_value;
}
}
}
else {
for (int cell=0; cell < numCells; ++cell) {
for (int qp=0; qp < numQPs; ++qp) {
Teuchos::Array<MeshScalarT> point(numDims);
for (int i=0; i<numDims; i++)
point[i] = Sacado::ScalarValue<MeshScalarT>::eval(coordVec(cell,qp,i));
yieldStrength(cell,qp) = exp_rf_kl->evaluate(point, rv);
}
}
}
if (isThermoElastic) {
for (int cell=0; cell < numCells; ++cell) {
for (int qp=0; qp < numQPs; ++qp) {
yieldStrength(cell,qp) -= dYdT_value * (Temperature(cell,qp) - refTemp);
if (print)
{
std::cout << " Y : " << yieldStrength(cell,qp) << std::endl;
std::cout << " temp: " << Temperature(cell,qp) << std::endl;
std::cout << " dYdT: " << dYdT_value << std::endl;
std::cout << " refT: " << refTemp << std::endl;
}
}
}
}
if (isDiffuseDeformation) {
Albany::MDArray CLold = (*workset.stateArrayPtr)[CLname];
for (int cell=0; cell < numCells; ++cell) {
for (int qp=0; qp < numQPs; ++qp) {
// yieldStrength(cell,qp) = constant_value*( 1.0 + (zeta-1.0)*CL(cell,qp) );
yieldStrength(cell,qp) -= constant_value*(zeta-1.0)*(CL(cell,qp) -CLold(cell,qp) );
if (print)
{
std::cout << " Y : " << yieldStrength(cell,qp) << std::endl;
std::cout << " CT : " << CT(cell,qp) << std::endl;
std::cout << " zeta : " << zeta << std::endl;
}
}
}
}
}
